9 Aug
2005
9 Aug
'05
11:29 p.m.
If f:F->E is a geometric morphism between elementary toposes then there is a, well known, adjunction Sigma_f -! f* between the category of locales internal to E and the category of locales internal to F. A property of this adjunction is that f* commutes with the upper (and lower) power locale functors. I think that this actually characterizes geometric morphisms: given an adjunction L-!R between locales internal in E and locales internal in F such that the right adjoint (R) commutes with the upper and lower power locales then there exists a geometric morphism, f:F->E such that L=Sigma_f and R=f*. Has anyone looked at this type of result before? Thanks, Christopher (Townsend)